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Statistical thinking in Medicine (Historical Overview)
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Statistical thinking in Medicine (Historical Overview)


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This is a talk I gave during the third year of my Residency in Internal Medicine at the University of Cincinnati. It goes over the history and evolution of statistical concepts underlying Medical …

This is a talk I gave during the third year of my Residency in Internal Medicine at the University of Cincinnati. It goes over the history and evolution of statistical concepts underlying Medical Science and Evidence Based Medicine

A nice summary (from which most of the material after Laplace's time came from) is given in:

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  • 1. Statistical Thinking In Medicine A brief history of statistical concepts endeavors in Medical Science Christos Argyropoulos MD, Cincinnati 29 th April 2005
  • 2. Permeation of Statistics in Modern Biomedicine
    • Statistical ideas, tools are paramount in conducting medical research “experiments”
    • NIH grant applications demand the incorporation of statistical considerations and require statisticians to be collaborators
    • Health Policy and Quality Improvement initiatives are motivated and enabled by quantitative arguments
    • Individual physicians are asked to utilize (or at least have an appreciation of) quantitative reasoning approaches to the interpretation of medical research in the Boards and the “real world”
    • How did we get here?
  • 3. Purpose of this presentation
    • Describe the historical evolution of ideas about statistical methods in Western Medicine and the culmination in the randomized control clinical trial
    • Demonstrate the two-way interaction between modern Medicine and Statistical Science
    • Understand the historical roots of controversies and ambivalences about modern evidence based medicine
  • 4. What is Medicine?
    • Medicine is both an area of knowledge (a science ), and the application of that knowledge
    • The science of medicine is the knowledge of body systems and diseases
    • T he profession of medicine refers to the social structure of the group of people formally trained to apply that knowledge
  • 6. What is Statistics?
    • Statistics is the science and practice of developing knowledge through the use of empirical quantitative data
    • R andomness and uncertainty are modelled by probability theory .
    • Statistical practice also involves rational decision making in situations of uncertainty
  • 8. The first clinical trial (606BC)
    • “ Prove thy servants, I beseech thee, ten days ; and let them give us pulse to eat, and water to drink.
    • Then let our countenances be looked upon before thee, and the countenance of the children that eat of the portion of the king’s meat: and as thou seest,deal with thy servants.
    • So he consented to them in this matter, and proved them ten days. And at the end of ten days their counte-nances appeared fairer and fatter in flesh than all the children which did eat the portion of the king’s meat.
    • Thus Melzar took away the portion of their meat, and the wine that they should drink and gave them pulse.
    • Quality Control questions about the Study:
    • Was there a stopping rule?
    • Why ten days?
    • What was the outcome measured (“fairness”)
    • Was there a discrete or continuous scale employed?
    • How were the inferences summarized?
    • Daniel may not be Fisher but
    • Use of experimental evidence to settle a (health-related) issue
    • Control group was employed (with similar characteristics?)
    • The evidence was used to change state policy and Daniel and his companions were allowed to continue their cosher diet
    • Red meat is bad for one’s health!
    Old Testament Book of Daniel Chapter 1 12-16
  • 9. Empiricism in Hippocratic Medicine (~400BC) I
    • Hippocrates: meticulous collection of clinical case descriptions and outcomes
    • Inductive approach to medical science
    • Semi-quantitative reasoning was applied i.e. “Those who are constitutionally very fat are more apt to die quickly than those who are thin” .
  • 10. Empiricism in Hippocratic Medicine (~400BC) II
    • “ Case-based reasoning” (CBR) can be either qualitative or quantitative
    • Hippocratic medicine has been claimed to “pro or anti EBM” by modern writers
    • Paradigm transferred to non-medical fields in the 80s-90s by Artificial Intelligence scientists
    • Modern CBR systems are used to solve problems in scientific – technical fields
  • 11. Stat Wars: The (Roman) Empire strikes back
    • For the next 500 years, the Hippocratic system of observation-based objects was the dominant scientific paradigm in medicine.
    • During the consolidation of the Roman Empire (1-200 AD) a number of “alternative” medical systems appeared and the orthodoxy was challenged
    • A 20 year old physician (who would later dominate medical thinking for a millennium) came to the rescue by raising questions about the evaluation of evidence
  • 12. Statistical Ideas in Galen’s work – The context
    • The dogmatists argued for the primacy of logical theories
    • The empiricists maintained that only data (in the form of clinical observations) and experimentation could serve the same goals
    • The empirico-rationalists supported a middle-out approach
  • 13. Statistical Ideas in Galen’s work – The context
    • Galen. (c. 150). Galen on Medical Experience Oxford: Oxford University Press, 1944.
    “ Experience” -> Observation -> Counts of Cases
  • 14. Probabilistic Ideas in Galen’s work I How can we assert that the empirical weight of evidence points towards a particular cause of a disease or an efficacious treatment? “ I assert that experience has shown that what has produced a like result in three cases can produce the reverse in three others. I say that a thing seen may be seen exactly as before, and yet belong to those things which are of both kinds, or to those things that happen often or to those things that take place but rarely. […] What is to prevent the medicine that is being tested from having a given effect on two hundred people and the reverse effect on twenty others ; and to prevent that of the first six people who were seen at first and on whom the remedy took effect, three belong to the two hundred and three to the twenty, without you being able to know which three belong to the two hundred and which to the twenty, even if you were a soothsayer? … Therefore I say of what has been seen but once , that it is not technical, just as the single grain of wheat is not a perfect heap; but if it is a thing that is seen many times in the same way , then I call it technical…”
  • 15. Statistical Ideas in Galen’s work II
    • Can one use finite number of observations to add to the weight of evidence?
    18 centuries before the work of Kiaer who stated that “the part (sample) can replace the whole (population)” a physician described the formal foundation of sample based inference and the need for representativeness
  • 16. Statistical Ideas in Galen’s work II
    • Can one use finite number of observations to add to the weight of evidence?
    “ Having learnt in advance from the works of nature you have already seen, you should hope that its art concerning all other [creatures] is the same. In the same way we form an opinion about the arts of people, because we do not expect to see all the statues that Phidias and Polycleitus had made, but from the ones we have seen, we hope the others [are the same], accordingly, the one who gained experience [in selecting] the works of nature, can conclude about [any other] from what he has already seen” Galen. De anatomicis administrationibus libri ix. In: Kühn CG. Claudii Galeni opera omnia , volume 2. Olms, Hildelsheim: 1964:545 pp. line 11-17.
  • 17. Statistical Ideas in Galen’s work II
    • Can one use finite number of observations to add to the weight of evidence?
    Galen. De sanitate tuenda libri vi. In Kuhn Corpus medicorum Graecorum, Koch K., Leipzig, 1923 vol. 6, p. 212, line 1 to p. 214, line 5. “ Theon (a contemporary gymnast) made a mistake by saying that hot baths are of great beneficence to all people, because Theon used hot baths after hard workouts. But he [made his observations] only on good athletes in very good shape who had hot baths after hard workouts and benefited from them “
  • 18. Statistical Ideas in Galen’s work III Extrapolating from a small group of cases can be dangerous “ […] But if it happened once in every three or four successful deliveries that the fetus be prevented [to exit the uterus because of its wrong position], it follows that in every four hundred fetuses one hundred will be prevented. But ... this is seen to happen once in multiple thousands ... ” Galen. De usu partium. In: Helmreich G.. Galeni de usu partium libri xvii . Hakkert, Amsterdam: 1968; volume 4, page 248, line 4-17.
  • 19. Statistical Ideas in Galen’s work III
    • In modern bio-statistical notation we express the same concepts as :
    • “ Let n denote the number of people in the sample studied, p the proportion of the sample possessing the characteristic under study, and P the underlying (but unknown) proportion who possess the characteristic. Inferences about P may be made using the binomial probability distribution …. A confidence interval may be assigned to the underlying proportion”
    • Joseph L Fleiss. Statistical methods for rates and proportions. Wiley Series in Probability and Mathematical Statistics. 1981 page 13, line 12-15
  • 20. Statistical Ideas in Galen’s work III
  • 21. Probabilistic Ideas in Galen’s work IV
    • highlight the significance of an experiment’s result repeatability in order to arrive at a reliable scientific conclusion
    • (“.. you must deny me faith in my words .. I transfer the authority to anyone who wishes, to come and show me if what I say concerning the findings of anatomies is really true. For I have already shown thousands of times … And this must be shown by anyone after I and my pupils have died “)
    Among other things, was probably the first to:
  • 22. Statistical Ideas in Galen’s work V
    • Understood that the definition of health v.s. disease is not always clear, and a quantitative definition might be required
    • “ So, what is the concept of a healthy body construction, and what of a diseased? The healthy one has all its systems functioning; the diseased, not functioning. But if someone who is healthy has his systems not functioning so well as someone else's, but not malfunctioning, he is said to have a bad constitution , not a disease. … So, it is necessary to define what is the amplitude of health, since there are many many differences between healthy bodies on its [health’s] upper and lower limits . “
    Among other things, was probably the first to:
  • 23. Statistical Ideas in Galen’s work VI
    • Provide the first statistical description of a medical object (i.e. the expected day of delivery)
    • “ For the seven month births I transfer my whole life's knowledge as I always very carefully acquainted the exact time of the conception of the sperm by women, which time if you ignore it is impossible to find the date of birth. And I found most of them between 190 and 200 days , a few of them some days earlier or some days later , but none before day 184 or after day 204 .”
    Among other things, was probably the first to: Galen. De septimestri partu. "Galenos' Schrift uber die Sieben-monatskinder". Quellen und Studien zur Geschichte der Naturwissenschaften und Medizin 3.4. 1933, 127-130
  • 24. Statistical Ideas in Galen’s work VII
    • The previous passage also demonstrates the use of quantitative data to define the boundaries of an object .
    • After defining the object in terms of a quantitative co-variate of its members, the former would become an independent entity for study.
    • It will take 1700 years for the same concepts to re-appear in the biomedical and social sciences with the creation of the “average man” by Quatelet and regression analysis by Galton
  • 25. Statistical Ideas in Galen’s work Epilogue
    • In his writings, Galen uses the word probability 300 times, without a formal (i.e. mathematical) framework.
    • The word admits both a “ degrees-of-belief” and “ frequency of event” interpretation .
    • Upper limit of qualitative approaches to uncertainty
  • 26. Enabling events of Modern Statistics
    • Over the next 1500 years, developments in science, technology and world-politics would enable the creation of statistical science.
    • Modern Numerals and zero (0-9) in India (~500 AD).
    • R ules for adding, subtracting, multiplying, and dividing ( Khowarizmi ~ AD 800 ) .
    • Introduction of the numerical system in Europe (Fibonacci 1202 AD)
  • 27. Enabling events of Modern Statistics
    • Over the next 1500 years, developments in science, technology and world-politics would enable the creation of statistical science.
    • Mercantilism and the birth of the “nation-state”
    • Gambling houses and casinos are established across Europe
    • Mathematical analysis and differential calculus ( Isaac Newton and Gottfried Wilhelm von Leibniz 17 th century)
  • 28. The birth of Probability
    • The concept of “probability” is grounded in mathematical (i.e. quantitative) terms in the 18 th century.
    • Probability = long-run frequency of an event (Bernoulli-law of large numbers)
    • Probability = degree of belief about an uncertain event (Laplace, Bayes - theorem).
  • 29. Bayes and his Theorem
    • "An Essay Toward Solving a Problem in the Doctrine of Chances" (Bayes 1764) ”
    • method by which we might judge concerning the probability that an event has to happen, in given circumstances, upon supposition that we know nothing concerning it but that, under the same circumstances, it has happened a certain number of times, and failed a certain other number of times.
  • 30. Bayes and his Theorem
    • Likelihood ratio (positive):
    • = Sensitivity/(1-Specificity)
    • = (TP/Disease +)/(FP/Disease –)
    • If ODDS = p(event)/[1-p(event)], then:
    • Pre-test odds x Likelihood ratio = Post-test odds
    • Prior odds x Likelihood ratio = Posterior odds
  • 31. “ Bedside” Bayes
    • These formulas are behind the clinical use of the PIOPED study data and the dreaded question by Nuclear Medicine physicians: “What’s your pre-test probability doc?”
    • Clinical use of any laboratory test can (and should) be guided by the interplay of test – characteristics (objectively quantifiable as sensitivity, specificity) and a subjective judgment (pre-test probability)
  • 32. Probabilistic inference in Medicine - the first years
    • Pierre-Simon Laplace : mathematical theory of scientific inference (18 th century)
    • Laplace applied his “hammer” to all sorts of “nails”: celestial mechanics, games of chance and …
    • Medicine (“the preferred method of treatment would manifest increasingly in the [probability] measure as the number of observations was increased”)
    Marquis de Laplace A philosophical Essay on Probabilities . English Translation Dover Publications ISBN 0486288757
  • 33. Probabilistic inference in Medicine - the first debate
    • Laplace’s view was hotly debated within the medical community
    • Pieere-Jean Georges Cabanis (1757-1808): proper professional behavior for a physician is to match the characteristics of each patient with the personal knowledge acquired through practice
    • Phillipe Pinel (1745-1726): the direct use of success-failure sample frequencies
  • 34. Case-Control Studies and Statistical Summaries
    • The first case-control (actually case series) study was conducted in Paris by Pierre-Charles-Alexandre Louis (1787–1872) between 1822-1827 during an outbreak of typhoid fever.
    • Case = fatal cases of typhoid (n=50, avg age=23)
    • Control = survivor of typhoid (n=88, avg age=21)
    • Hypothesis tested = efficacy of bloodletting (standard of treatment at that time)
    • Data reported : frequencies of the “exposure” factor i.e. bloodletting in survivors and non-survivors as well as the average survival time
    • Inferences : conducted on the basis of enumeration of the various outcomes (“numerical method”)
    • Conclusion = bloodletting NOT helpful
    Louis, P. C. A. (1836). Anatomical, Pathological and Therapeutic Researches upon the Disease Known under the Name of Gastro-Enterite Putrid, Adynamic, Ataxic, or Typhoid Fever, etc., Compared with the Most Common Acute Diseases, Vols. 1 and 2, trans. Henry I. Bowditch. Issac R. Butts, Boston.
  • 35. Case-Control Studies and Statistical Summaries Survivors Yes No BLOOD-LETTING YES 62 39 NO 26 13
  • 36. Case-Control Studies and Statistical Summaries
    • If we were given the same data today, we would summarize our inferences in the following way:
    • the OR for the exposure (“bloodletting”) is 1.258, with a 95% CI of 0.578-2.736
    • Χ 2 = 0.148 with a p value of 0.701
  • 37. Early American “EBM” I
    • Louis work was not received well
    • However he spread the word to the foreign students who flocked to Paris, attracted by his approach .
    • Two of his most enthusiastic students were William Gerhard and Caspar Pennock of Philadelphia who applied the methods to study an epidemic of highly malignant fever
    • T heir study provided the earliest differentiation of typhus from typhoid
  • 38. Early American “EBM” II
    • In 1843 Austin Flint in Buffalo, concluded that typhoid was spread by contagion which he suspected was carried by water.
    • Oliver Wendell Holmes used Louis' method and an actuary to rule out chance as an explanation for spread of puerperal fever
    • Frank Hastings Hamilton applied the numerical method to his own practice (“fracture tables”)
  • 39. The early appearance of the “P-value” I
    • The ideas of Louis, were applied 10 years later in another problem, the comparison of two competing therapies
    • The disease: Bladder Stones
    • “ Standard of Care” = Open surgical extraction of stones
    • Modern Treatment = Lithotrity
    • The death rate of the old procedure was 21.6% (1,237/5,715); the death rate for lithotrity was 2.3% (6/257)
    • The surgeon Jean Civalie argues for abandoning the old procedure
  • 40. The early appearance of the “P-value” II
    • The French Academy of Sciences and Medicine appoints a committee to investigate the findings of Civalie
    • T he mathematician Simeon-Denis Poisson (1781–1840) argues for the application of the law of large numbers
    • T he physician Francois Double (1776–1842) argued that the whole method was inappropriate to “ elevate t he human spirit to that mathematical certainty found only in astronomy ”
  • 41. The early appearance of the “P-value” III
    • Issue is finally settled by Louis-Denis-Jules Gavarret (1809–1890) who had trained both as engineer and physician
    • P robability theory merely expresse s the statistical results of inductive reasoning in a more formal and exact manner
    • S tatistical results are useful only if , the cases are similar or comparable, and there must be many such observation s
  • 42. The early appearance of the “P-value” IV
    • Precision to be sought after is the 99.5% favoring the new treatment versus the standard (the posterior Probability favoring Lithotrity was <0.0001)
    • Used the same argument to criticize the small number of observations in Louis studies on pneumonia, TB and typhoid
    • In Germany, the ophthalmologist Julius Hirschberg (1843–1925), concerned about the number of observations required by Gavarret’s assumption of 212:1 odds, modified the formula by using a lower standard of confidence of 11:1 or 91.6%.
    • Eventually the standard would rise to the 95%, a number that would attain religious belief status
  • 43. The “death” of the first period of “EBM”
    • With the retirement of Louis in the mid-1850s, his influence begins to fade away
    • Birth of modern Experimental and Laboratory medicine, by Pasteur - Koch (“germ theory”) and Claude Bernard (“physiology”)
    • Experimental investigation of each individual patient could provide an “objective” scientific
    • Valid “scientific” results consists of the discovery of causation, not just the discovery of the correlation [Friedrich Oesterlen (1812–1877)]
  • 44. First synthetic attempts fail
    • Carl Wunderlich (1815–1877) : collection of massive datasets of quantifiable physiological data
    • P rincipal contribution was the establishment of a range of normal temperature from 36.3 to 37.5°C which was compiled from 1 million readings in over 25,000 patients
    • Fever IS a symptom NOT a disease
    Valid scientific program in 21st century
  • 45. First synthetic attempts fail Valid scientific program in 21st century
  • 46. Curtain: The “numerical” method
    • Joseph Lister (1827–1912) publishe s his pioneering work with antiseptic surgery in 1870
    • A verage mortality rate was 45.7% (16/35) for all surgical procedures performed at the University of Edinburgh in the years 1864–1866
    • Reports that it was 15% (6/40) for all surgical procedures performed in the three-year period 1867–1869.
    • Although he used this statistical result to show the efficacy of the new antiseptic method, he claimed that the science behind this was the germ theory of disease as proposed by Louis Pasteur (1822–1895) and not the numbers!
  • 47. Statistical Developments of the late 19 th Century – Early 20 th Century
    • 1877 -- F. Galton -- regression to the mean
    • 1888 -- F. Galton -- correlation
    • 1900 -- Karl Pearson -- chi square; applied correlation to natural selection
    • 1908 -- &quot;Student&quot; (W. S. Gossett) -- T he t-test
    • 1919 --  R. A. Fisher -- ANOVA
    • 1930's -- Jerzy Neyman and Egon Pearson -- type II errors, power of a test, confidence intervals
    • 1920s-1940s -- Quantum mechanics and the need to model outcomes of repetitive experiments -- “long-run frequency” interpretation of probability
  • 48. The birth of Medical Statistics I
    • Heavily influenced by Karl Pearson, who similarly to Louis would try to “spread the word” through his students. They would go to subsequently establish the first statistic departments in Medical/Public Health Schools
    • Major Greenwood (1880–1949) makes the distinction between a “ mathematical error ” (measurement error) and “ functional error ” ( Lister Institute for Preventive Medicine in 1903 )
    • Raymond Pearl (1879–1940) : The Johns Hopkins University as professor of biometry and vital statistics in the School of Hygiene and Public Health
  • 49. The birth of Medical Statistics II
    • Sir Ronald A. Fisher (1890–1962) statistical methods for design and analysis of experiments.
      • replication
      • randomization ,
      • organization of the data gathering aspect of the experiment
    Fisher, R. A. (1958). Statistical Methods for Research Workers, 13th edn.,Hafner, New York. “ To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of”
  • 50. The First Modern Clinical Trial I
    • Sponsored in 1946 by the British Medical Research Council
    • Study Question: Is Streptomycin an effective TB treatment?
    • Study Design: Randomized, controlled, multi-center comparison between two groups
    • Treatment Group : Streptomycin + Bed Rest
    • Control Group: Bed Rest alone (Standard of Care)
  • 51. The First Modern Clinical Trial II
    • End Points:
      • Radiographic Improvement (assessed by two Radiologists and an Internist “ without knowledge of whether the films being viewed were those of S or C patients ”)
      • Differences in interpretation of XRs resolved by review session
      • Patient Survival
    • MRC. (1948). Streptomycin treatment of pulmonary tuberculosis: A Medical Research Council Investigation, Br. Med. J. ii : 769-782 h ttp://
  • 52. The First Modern Clinical Trial III
    • Enrollment : January 1947 – September 1947
    • Number of patients enrolled : 55 (S), 52(C)
    • Study Results:
    • “ Four of the 55 S patients (7%) and 14 of the 52 C patients (27%) died before the end of six months. The difference between the two series is statistically significant; the probability of it occurring by chance is less than one in a hundred ”
    • MRC. (1948). Streptomycin treatment of pulmonary tuberculosis: A Medical Research Council Investigation, Br. Med. J. ii : 769-782 h ttp://
  • 53. Summary and Conclusion
    • Statistical Ideas and Applications in Medicine are not the invention of the 20 th century
    • Physicians entertained the idea that medical knowledge can be understood in quantitative terms thousands of years ago
    • However there has always been a significant resistance in accepting the idea, in spite of its effectiveness in practice (i.e. The limits of evidence-based medicine. R espir Care. 2001 Dec;46(12):1435-4 for a modern version of the same arguments)